Let an denote the solutions of n = x1 + x2 where x1, x2 are natural numbers and x2 is an even number.
I need to show that the generating function of an is of the form:
(1 + x + x^2 + x^3 + ...)(1 + x^2 + x^4 + x^6 + ...) = 1/[(1-x)(1-x^2)]
I ultimately want to find a closed formula for an. However I would like to prove the above first before I go about doing that. Any ideas would be great. Thanks!